How to create a simple extruded box model?
What you are asking for is not one tool but a workflow. There is no one set way to do this, curves can be better for getting rounded edges but mesh modeling can be just as good.

However, this is fairly simple and you can achieve the majority of what you ask by just extruding. You can extrude faces, edges and vertices in Blender with the Extrude tool. Just select a face, vertex or edge and press E.

(Alternatively, you can constrain your extrusions to extruding along the object normal with Alt + E), you can experiment with this.

I will use the image you provided as a quick example here..

First, get as close as you can to the shape of the object, (I create the outline of the object from top view). I add a plane  and just grab the edges and subdivide a few times using W > Subdivide while in Edit mode to get some more geometry. I then move the new vertices to fit the shape of the image as closely as possible. To make it more detailed and organic as you ask, you can add more vertices to round out the curved side.



If the face has not been filled, you can use F to make a face from several vertices. I then extrude and delete the top face to give it some depth. To get the lid, I just duplicated the object with Shift+E and moved the sides down.



You can take it anywhere from here now.. I have also quickly added a Solidify modifier to give it some thickness. Also another note, I wouldn't worry too much as a beginner on getting accurate units etc, If you insist however, you can change the units using the Scene tab under Units.

To carry on, I recommend that you see these:


How can I make sharp geometric 3d models look more realistic?
Most efficient way to round edges
When should N-Gons be used, and when shouldn&#39;t they?